Six Sigma is a well-recognized quality management system that employs improvement projects to improve business processes to reduce product and service defects, reduce costs, and increase profits. Each project has a “champion” from upper management who is responsible for the project’s success. The project leader is known as a “black belt,” and project team members are called “green belts.” Simsun, a manufacturer of cell phone parts and components has eight improvement projects under consideration, and six champions, 10 black belts, and 25 green belts available to be assigned to the projects. The following table shows for each of the projects the number of green belts required, the percent reduction in defects expected, the cost savings (in $ millions), and the profit improvement (in $ millions).

The company wants to select the projects that will result in the greatest profit improvement while achieving a defect reduction of at least 5 percent and cost savings of at least $6.3 million. Formulate and solve an integer programming model for this problem.

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Project 1 2 3 4 5 6 7 8 Green Belts 3 4 7 2 6 5 4 6 Defect Reduction (%) 0.97 1.35 1.16 0.82 1.02 0.86 1.15 0.96 Cost Savings (SM) 1.32 1.16 0.95 0.88 1.05 1.26 1.13 0.85 Profit Improvements ($ M) 1.9 2.3 3.6 2.7 4.1 3.8 5.3 4.8